Firefox worked yesterday morning but not in the afternoon. G-mail also does not work now.

Firefox screen now different including a caution sign and e-mail address www.Personalinteractive.com at the top. Indicates I am on an old version but when I try to update it indicates my operating system is not adequate. We have an apple laptop running OS X 10.5.8. Also g-mail will not open. Does not accept password.

Firefox screen now different including a caution sign and e-mail address www.Personalinteractive.com at the top. Indicates I am on an old version but when I try to update it indicates my operating system is not adequate. We have an apple laptop running OS X 10.5.8. Also g-mail will not open. Does not accept password.

Last but not least, can you think of any software you installed between the last time you started Firefox (things working normally) and this time? That software might be the problem and might need to be removed in order to avoid having your Firefox settings changed again.

Any luck?

First, could you check for unexpected/unwanted extensions here:
Tools menu > Add-ons > Extensions category
I suggesting disabling ALL nonessential extensions (i.e., extensions you do not use at least daily) then restarting Firefox.
To reset your home page to what you had before, you can use this dialog:
Firefox > Preferences > General
The following article suggests different ways to do that: [[How to set the home page]].
The last version of Firefox that ran on MacOS X 10.5.x was Firefox 16. You definitely do not want to be running Firefox 3.6.6. Could you check your true version here:
Help > About Firefox
If that dialog shows Firefox 16, then the information that your browser reports to websites is incorrect. This article describes how you can correct that: [[Websites say that Firefox is outdated or incompatible even though it's the latest version]].
Last but not least, can you think of any software you installed between the last time you started Firefox (things working normally) and this time? That software might be the problem and might need to be removed in order to avoid having your Firefox settings changed again.
Any luck?

If it turns out you need a fresh installer for Firefox 16.0.2, open this article, and look for the link under "I still want to downgrade": Install an older version of Firefox.

Please note the security warning! You might be opening yourself up to another episode of strange happenings on your system...

If it turns out you need a fresh installer for Firefox 16.0.2, open this article, and look for the link under "I still want to downgrade": [[Install an older version of Firefox]].
Please note the security warning! You might be opening yourself up to another episode of strange happenings on your system...